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ITERATION OF QUADRATIC POLYNOMIALS OVER FINITE FIELDS
Author(s) -
HeathBrown D. R.
Publication year - 2017
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579317000328
Subject(s) - iterated function , mathematics , cardinality (data modeling) , finite field , sequence (biology) , quadratic equation , field (mathematics) , value (mathematics) , pure mathematics , discrete mathematics , mathematical analysis , statistics , genetics , geometry , biology , computer science , data mining
For a finite field of odd cardinality q , we show that the sequence of iterates of a X 2 + c , starting at 0 , always recurs after O ( q / log log q ) steps. ForX 2 + 1 , the same is true for any starting value. We suggest that the traditional “birthday paradox” model is inappropriate for iterates ofX 3 + c , when q is 2 mod 3.
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